Decision support techniques have a key role in investment and strategic decisions in the energy sector. As complex decision-making problems involve the simultaneous consideration of an extensive set of different factors, it is an essential part of the methodology to define, structure, and integrate the criteria. The main purpose of the study was to develop a system of criteria and weights that are suitable for general application in the energy sector and can best describe the decision-making mechanisms present in society and various social groups. When developing the system of criteria, we moved away from the hierarchical approach related to the three pillars of sustainability; therefore, a wide range of notions were assessed based on a population representative survey data collected in Hungary. We used algebraic methods to explore the internal structure of the set of criteria that had been previously defined by means of social sciences, while the importance weights were specified by applying the method of analytic network process. Furthermore, the ranking of heating and electricity generation alternatives were determined.